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Sound Transmission Loss Analysis of a Double Plate-Acoustic Cavity Coupling System with In-Plane Functionally Graded Materials
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作者 Changzhong Chen Mingfei Chen Wenliang Yu 《Journal of Applied Mathematics and Physics》 2024年第6期2333-2345,共13页
In this paper, the isogeometric analysis (IGA) is employed to develop an acoustic radiation model for a double plate-acoustic cavity coupling system, with a focus on analyzing the sound transmission loss (STL). The fu... In this paper, the isogeometric analysis (IGA) is employed to develop an acoustic radiation model for a double plate-acoustic cavity coupling system, with a focus on analyzing the sound transmission loss (STL). The functionally graded (FG) plate exhibits a different material properties in-plane, and the power-law rule is adopted as the governing principle for material mixing. To validate the harmonic response and demonstrate the accuracy and convergence of the isogeometric modeling, ANASYS is utilized to compare with numerical examples. A plane wave serves as the acoustic excitation, and the Rayleigh integral is applied to discretize the radiated plate. The STL results are compared with the literature, confirming the reliability of the coupling system. Finally, the investigation is conducted to study impact of cavity depth and power-law parameter on the STL. 展开更多
关键词 Isogeometric Analysis Sound Transmission Loss Double-plate System functionally graded materials Acoustic Structure Coupling
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3D analytical solution for a rotating transversely isotropic annular plate of functionally graded materials 被引量:2
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作者 CHEN Jiang-ying CHEN Wei-qiu 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2007年第7期1038-1043,共6页
The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded tra... The analytical solution for an annular plate rotating at a constant angular velocity is derived by means of direct displacement method from the elasticity equations for axisymmetric problems of functionally graded transversely isotropic media. The displacement components are assumed as a linear combination of certain explicit functions of the radial coordinate, with seven undetermined coefficients being functions of the axial coordinate z. Seven equations governing these z-dependent functions are derived and solved by a progressive integrating scheme. The present solution can be degenerated into the solution of a rotating isotropic functionally graded annular plate. The solution also can be degenerated into that for transversely isotropic or isotropic homogeneous materials. Finally, a special case is considered and the effect of the material gradient index on the elastic field is illustrated numerically. 展开更多
关键词 functionally graded materials Transversely isotropic Rotating annular plate Analytical solution
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3D thermally induced analysis of annular plates of functionally graded materials 被引量:2
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作者 Yun-Fang Yang Ding Chen Bo Yang 《Theoretical & Applied Mechanics Letters》 CAS CSCD 2019年第5期297-301,I0004,共6页
Within the framework of three-dimensional elasticity theory,this paper investigates the thermal response of functionally graded annular plates in which the material can be transversely isotropic and vary along the thi... Within the framework of three-dimensional elasticity theory,this paper investigates the thermal response of functionally graded annular plates in which the material can be transversely isotropic and vary along the thickness direction in an arbitrary manner.The generalized Mian and Spencer method is utilized to obtain the analytical solutions of annular plates under a through-thickness steady temperature field.The present analytical solutions are validated through comparisons against those available in open literature.A parametric study is conducted to examine the effects of gradient distribution,different temperature fields,different diameter ratio and boundary conditions on the deformation and stress fields of the plate.The results show that these factors can have obvious effects on the thermo-elastic behavior of functionally gradient materials(FGM)annular plates. 展开更多
关键词 ANNULAR plate functionally graded materials THERMO-ELASTICITY ANALYTICAL SOLUTION
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AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES 被引量:6
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作者 Guojun Nie Zheng Zhong 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第4期289-295,共7页
Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using ... Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials. 展开更多
关键词 two-directional functionally graded materials circular and annular plates axisym-metric bending semi-analytical numerical method integrated design
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Pure bending of simply supported circular plate of transversely isotropic functionally graded material 被引量:6
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作者 LI Xiang-yu DING Hao-jiang CHEN Wei-qiu 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2006年第8期1324-1328,共5页
This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial d... This paper considers the pure bending problem of simply supported transversely isotropic circular plates with elastic compliance coefficients being arbitrary functions of the thickness coordinate. First, the partial differential equation, which is satisfied by the stress functions for the axisymmetric deformation problem is derived. Then, stress functions are obtained by proper manipulation. The analytical expressions of axial force, bending moment and displacements are then deduced through integration. And then, stress functions are employed to solve problems of transversely isotropic functionally graded circular plate, with the integral constants completely determined from boundary conditions. An elasticity solution for pure bending problem, which coincides with the available solution when degenerated into the elasticity solutions for homogenous circular plate, is thus obtained. A numerical example is finally presented to show the effect of material inhomogeneity on the elastic field in a simply supported circular plate of transversely isotropic functionally graded material (FGM). 展开更多
关键词 Transversely isotropic functionally graded materials (FGMs) Pure bending problem Simply supported circular plate Axisymmetric deformation
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Free vibration of functionally graded sandwich plates using four-variable refined plate theory 被引量:1
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作者 L.HADJI H.A.ATMANE +2 位作者 A.TOUNSI I.MECHAB E.A.ADDA BEDIA 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第7期925-942,共18页
This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown fu... This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates. 展开更多
关键词 functionally graded material (FGM) free vibration sandwich plate refinedplate theory (RPT) Navier solution
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FREE VIBRATION OF FUNCTIONALLY GRADED, MAGNETO-ELECTRO-ELASTIC, AND MULTILAYERED PLATES 被引量:7
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作者 Chen Jiangyi Chen Hualing Pan Ernian 《Acta Mechanica Solida Sinica》 SCIE EI 2006年第2期160-166,共7页
The state-space method is employed to evaluate the modal parameters of functionally graded, magneto-electro-elastic, and multilayered plates. Based on the assumption that the properties of the functionally graded mate... The state-space method is employed to evaluate the modal parameters of functionally graded, magneto-electro-elastic, and multilayered plates. Based on the assumption that the properties of the functionally graded material are exponential, the state equation of structural vibration which takes the displacement and stress of the structure as state variables is derived. The natural frequencies and modal shapes are calculated based on the general solutions of the state equation and boundary conditions given in this paper. The influence of the functionally graded exponential factor on the elastic displacement, electric, and magnetic fields of the structure are discussed by assuming a sandwich plate model with different stacking sequences. 展开更多
关键词 functionally graded material magneto-electro-elastic plates modal shapes statespace method
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THREE-DIMENSIONAL ANALYSIS OF FUNCTIONALLY GRADED PLATE BASED ON THE HAAR WAVELET METHOD 被引量:2
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作者 Zhang Chun Zhong Zheng 《Acta Mechanica Solida Sinica》 SCIE EI 2007年第2期95-102,共8页
A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. Wit... A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. With good features in treating singularities, Haar series solution converges rapidly for arbitrary distributions, especially for the case where the material properties change rapidly in some regions. Through numerical examples the influences of the ratio of material constants on the top and bottom surfaces and different material gradient distributions on the structural response of the plate to mechanical stimuli are studied. 展开更多
关键词 functionally graded material rectangular plate Haar wavelet three-dimensional analysis
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Thermal buckling analysis of ceramic-metal functionally graded plates 被引量:3
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作者 Ashraf M. Zenkour Daoud S. Mashat 《Natural Science》 2010年第9期968-978,共11页
Thermal buckling response of functionally graded plates is presented in this paper using sinusoidal shear deformation plate theory (SPT). The material properties of the plate are assumed to vary according to a power l... Thermal buckling response of functionally graded plates is presented in this paper using sinusoidal shear deformation plate theory (SPT). The material properties of the plate are assumed to vary according to a power law form in the thickness direction. Equilibrium and stability equations are derived based on the SPT. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The buckling analysis of a functionally graded plate under various types of thermal loads is carried out. The influences of many plate parameters on buckling temperature difference will be investigated. Numerical results are presented for the SPT, demonstrating its importance and accuracy in comparison to other theories. 展开更多
关键词 Thermal BUCKLING NON-LINEAR STRAINS functionally graded MATERIAL Sinusoidal plate
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Nonlinear oscillations of sigmoid functionally graded material plates moving in longitudinal direction 被引量:1
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作者 Yanqing WANG J.W.ZU 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2017年第11期1533-1550,共18页
Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material (S-FGM) plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along th... Geometrically nonlinear oscillations are investigated on sigmoid functionally graded material (S-FGM) plates with a longitudinal speed. The material properties of the plates obey a sigmoid distribution rule along the thickness direction. Based on the D'Alembert's principle, a nonlinear equation of motion is derived for the moving S-FGM plates, where the von K^rm^n nonlinear plate theory is adopted. Utilizing the Galerkin method, the equation of motion is discretized and solved via the method of harmonic bal- ance. The approximate analytical solutions are validated through the adaptive step-size fourth-order Runge-Kutta method. Besides, the stability of the steady-state solutions is examined. The results reveal that the mode interaction behavior can happen between the first two modes of the moving S-FGM plates, leading to a complex nonlinear frequency response. It is further found that the power-law index, the longitudinal speed, the exci- tation amplitude, and the in-plane pretension force can significantly affect the nonlinear frequency-response characteristics of longitudinally traveling S-FGM plates. 展开更多
关键词 sigmoid functionally graded material (S-FGM) plate MOVING nonlinearoscillation method of harmonic balance frequency response
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Several three-dimensional solutions for transversely isotropic functionally graded material plate welded with circular inclusion 被引量:1
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作者 Bo YANG Weiqiu CHEN Haojiang DING 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第6期683-694,共12页
The problem of a transversely isotropic functionally graded material (FGM) plate welded with a circular inclusion is considered. The analysis starts with the general- ized England-Spencer plate theory for transverse... The problem of a transversely isotropic functionally graded material (FGM) plate welded with a circular inclusion is considered. The analysis starts with the general- ized England-Spencer plate theory for transversely isotropic FGM plates, which expresses a three-dimensional (3D) general solution in terms of four analytic functions. Several analytical solutions are then obtained for an infinite FGM plate welded with a circular inclusion and subjected to the loads at infinity. Three different cases are considered, i.e., a rigid circular inclusion fixed in the space, a rigid circular inclusion rotating about the x-, y-, and z-axes, and an elastic circular inclusion with different material constants from the plate itself. The static responses of the plate and/or the inclusion are investigated through numerical examples. 展开更多
关键词 plate functionally graded material (FGM) welded circular inclusion analytical solution
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Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates
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作者 张鹤 蒋吉清 张治成 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第11期1467-1478,共12页
Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method (SSDQM). The p... Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method (SSDQM). The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model (ALM) is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated. 展开更多
关键词 functionally grade material thick plate three-dimensional solution semianalytical approach
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On asymmetric bending of functionally graded solid circular plates
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作者 Yingwu YANG Ying ZHANG +1 位作者 Weiqiu CHEN Bo YANG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2018年第6期767-782,共16页
Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied... Based on the three-dimensional elasticity equations, this paper studies the elastic bending response of a transversely isotropic functionally graded solid circular plate subject to transverse biharmonic forces applied on its top surface. The material prop- erties can continuously and arbitrarily vary along the thickness direction. By virtue of the generalized England's method, the problem can be solved by determining the expres- sions of four analytic functions. Expanding the transverse loarl in Fourier series along the circumferential direction eases the theoretical construction of the four analytic functions for a series of important biharmonic loads. Certain boundary conditions are then used to determine the unknown constants that are involved in the four constructed analytic functions. Numerical examples are presented to validate the proposed method. Then, we scrutinize the asymmetric bending behavior of a transversely isotropic functionally graded solid circular plate with different geometric and material parameters. 展开更多
关键词 functionally graded material circular plate transversely isotropic bihar-monic load elasticity solution
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Accurate Free Vibration of Functionally Graded Skew Plates
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作者 Jin Chunhua Wang Xinwei 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI CSCD 2017年第2期188-194,共7页
The present study aims to analyze free vibration of thin skew plates made of functionally graded material(FGM)by using the weak form quadrature element method.The material properties vary continuously through the thic... The present study aims to analyze free vibration of thin skew plates made of functionally graded material(FGM)by using the weak form quadrature element method.The material properties vary continuously through the thickness according to a power-law form.A novel FGM skew plate element is formulated according to the neutral surface based plate theory and with the help of the differential quadrature rule.For verifications,Numerical results are compared with available data in literature.Results reveal that the non-dimensional frequency parameters of the FGM skew plates are independent of the power-law exponent and always proportional to those of homogeneous isotropic ones when the coupling and rotary inertias are neglected.In addition,employing the physical neutral surface based plate theory is equivalent to using the middle plane based plate theory with the reduced flexural modulus matrix. 展开更多
关键词 functionally graded material(FGM) skew plate free vibration quadrature element method neutral surface
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Higher-order crack tip fields for functionally graded material plate with transverse shear deformation
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作者 Dianhui HOU Xiao CHONG +1 位作者 Guixiang HAO Yao DAI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2016年第6期695-706,共12页
The crack tip fields are investigated for a cracked functionally graded material (FGM) plate by Reissner's linear plate theory with the consideration of the transverse shear deformation generated by bending. The el... The crack tip fields are investigated for a cracked functionally graded material (FGM) plate by Reissner's linear plate theory with the consideration of the transverse shear deformation generated by bending. The elastic modulus and Poisson's ratio of the functionally graded plates are assumed to vary continuously through the coordinate y, according to a linear law and a constant, respectively. The governing equations, i.e., the 6th-order partial differential equations with variable coefficients, are derived in the polar coordinate system based on Reissner's plate theory. Furthermore, the generalized displacements are treated in a separation-of-variable form, and the higher-order crack tip fields of the cracked FGM plate are obtained by the eigen-expansion method. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with Reissner's effect when the in-homogeneity parameter approaches zero. 展开更多
关键词 crack tip field Reissner's effect plate functionally graded material (FGM) eigen-expansion method
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An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model 被引量:5
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作者 GAO LiMing WANG Ji +1 位作者 ZHONG Zheng DU JianKe 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS 2008年第2期165-175,共11页
In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functio... In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functionally graded material (FGM), the symmetry of modes and frequency behavior will be modified, thus producing dif-ferent features for engineering applications such as amplifying or reducing the velocity and deformation. This kind of effect can also be easily realized by utilizing a layered structure with desired material properties that can produce these effects in terms of velocity and displacements, since Rayleigh waves in a solid with gen-eral material property grading schemes are difficult to analyze with known methods. Solutions from layered structures with exponential and polynomial property grad-ing schemes are obtained from the layered model and comparisons with known analytical results are made to validate the method and examine possible applica-tions of such structures in engineering. 展开更多
关键词 RAYLEIGH WAVE surface acoustic WAVE vibration plate LAYERED structure functionally graded material (FGM)
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NONLINEAR DYNAMICS OF A FGM PLATE WITH TWO CLAMPED OPPOSITE EDGES AND TWO FREE EDGES 被引量:1
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作者 Y.X.Hao W.Zhang J.Yang 《Acta Mechanica Solida Sinica》 SCIE EI CSCD 2014年第4期394-406,共13页
This paper deals with the nonlinear forced vibration of FGM rectangular plate with a boundary of two edges clamped opposite and the other two free. The plate is subjected to transversal and in-plane excitations. The p... This paper deals with the nonlinear forced vibration of FGM rectangular plate with a boundary of two edges clamped opposite and the other two free. The plate is subjected to transversal and in-plane excitations. The present research treats the material properties of the FGM plates as temperature-dependent and graded continuously throughout the thickness direction, following the volume fraction of the constituent materials according to the power law. The temperature is assumed to be constant in the plane and varied only in the thickness direction of the plate. In the framework of geometrical nonlinearity the plate is modeled and the equations of motion are obtained on Hamilton's principle. With the help of Galerkin discretization, the nonlinear ordinary differential equations describing transverse vibration of the plate are proposed. By the numerical method, the nonlinear dynamical responses of the FGM plate with two clamped opposite and two free edges are analyzed. 展开更多
关键词 functionally graded materials plate clamped bifurcation
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Nonlinear dynamic analysis of moving bilayer plates resting on elastic foundations 被引量:3
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作者 M.ESMAEILZADEH M.KADKHODAYAN +1 位作者 S.MOHAMMADI G.J.TURVEY 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2020年第3期439-458,共20页
The aim of this study is to investigate the dynamic response of axially moving two-layer laminated plates on the Winkler and Pasternak foundations. The upper and lower layers are formed from a bidirectional functional... The aim of this study is to investigate the dynamic response of axially moving two-layer laminated plates on the Winkler and Pasternak foundations. The upper and lower layers are formed from a bidirectional functionally graded(FG) layer and a graphene platelet(GPL) reinforced porous layer, respectively. Henceforth, the combined layers will be referred to as a two-dimensional(2D) FG/GPL plate. Two types of porosity and three graphene dispersion patterns, each of which is distributed through the plate thickness,are investigated. The mechanical properties of the closed-cell layers are used to define the variation of Poisson’s ratio and the relationship between the porosity coefficients and the mass density. For the GPL reinforced layer, the effective Young’s modulus is derived with the Halpin-Tsai micro-system model, and the rule of mixtures is used to calculate the effective mass density and Poisson’s ratio. The material of the upper 2D-FG layer is graded in two directions, and its effective mechanical properties are also derived with the rule of mixtures. The dynamic governing equations are derived with a first-order shear deformation theory(FSDT) and the von Kármán nonlinear theory. A combination of the dynamic relaxation(DR) and Newmark’s direct integration methods is used to solve the governing equations in both time and space. A parametric study is carried out to explore the effects of the porosity coefficients, porosity and GPL distributions, material gradients, damping ratios, boundary conditions, and elastic foundation stiffnesses on the plate response. It is shown that both the distributions of the porosity and graphene nanofillers significantly affect the dynamic behaviors of the plates. It is also shown that the reduction in the dynamic deflection of the bilayer composite plates is maximized when the porosity and GPL distributions are symmetric. 展开更多
关键词 moving laminated plate bidirectional functionally graded material(FGM) graphene nanoplatelet POROSITY first-order shear deformation theory(FSDT) Newmark’s integration method
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Free vibration of functionally graded sandwich plates in thermal environments 被引量:2
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作者 Dongdong Li Zongbai Deng Guoping Chen 《International Journal of Mechanical System Dynamics》 2023年第1期39-47,共9页
This paper presents an analytical solution for the free vibration of functionally graded material(FGM)sandwich plates in a thermal environment.An equivalentsingle‐layer(ESL)plate theory with four variables is used to... This paper presents an analytical solution for the free vibration of functionally graded material(FGM)sandwich plates in a thermal environment.An equivalentsingle‐layer(ESL)plate theory with four variables is used to obtain the solution.Two types of sandwich plates are examined in this study:one with FGM face sheets and a homogeneous core and the other with an FGM core and homogeneous face sheets.The governing equations of motion are derived based on Hamilton's principle and then solved using the Navier method.The results of natural frequencies of simply supported FGM sandwich plates are compared with the available solutions in the literature.The effects of volume fraction distribution,geometrical parameters,and temperature increments on the free vibration characteristics are discussed in detail. 展开更多
关键词 functionally graded material sandwich plate equivalent‐single‐layer theory free vibration
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Closed-form solutions for free vibration of rectangular FGM thin plates resting on elastic foundation 被引量:4
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作者 T. F. Xu Y. F. Xing 《Acta Mechanica Sinica》 SCIE EI CAS CSCD 2016年第6期1088-1103,共16页
This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on class... This article presents closed-form solutions for the frequency analysis of rectangular functionally graded material (FGM) thin plates subjected to initially in-plane loads and with an elastic foundation. Based on classical thin plate theory, the governing differential equations are derived using Hamilton's principle. A neutral surface is used to eliminate stretching-bending coupling in FGM plates on the basis of the assumption of constant Poisson's ratio. The resulting governing equation of FGM thin plates has the same form as homogeneous thin plates. The separation-of-variables method is adopted to obtain solutions for the free vibration problems of rectangular FGM thin plates with separable boundary conditions, including, for example, clamped plates. The obtained normal modes and frequencies are in elegant closed forms, and present formulations and solutions are validated by comparing present results with those in the literature and finite element method results obtained by the authors. A parameter study reveals the effects of the power law index n and aspect ratio a/b on frequencies. 展开更多
关键词 functionally graded material Free vibration Rectangular plate Close form solutions Neutral surface
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